A quick visit to the Nasonex website found two good images of the bee to critique.
1) The eyes are clearly vertebrate-style eyes. Insect eyes do not have an iris, pupil, or sclera, and instead have compound eyes containing many ommatidia.
2) The legs are in the wrong place. All insect legs and wings arise from the thorax (the middle tagma), but instead this bee has been drawn with two pairs of legs coming off the abdomen. Only certain other arthropods (e.g. crustaceans) have appendages on their abdomens.
3) The mouth is wrong, wrong, wrong. Insects do not have teeth and do not have a jaw (both of these are uniquely chordate characteristics). Bees also do not have chordate-style tongues, which it appears that this bee has. Instead, bees have both mandibles and a tube that protrudes from their head and contains a tongue-like structure (formed from modified arthropod mouthparts; two maxillae and the labial palps wrapping around a glossa). The jaw and teeth this bee has been drawn with would be decidedly useless in consuming nectar and honey, two of a honey bee's primary food sources.
4) The bee is alternately drawn with one or no pairs of wings. When the bee first loads on their site, it somehow flies across the screen with a complete lack of wings. When the bee reappears, it has only one pair of wings. I'm sure the bee would be highly insulted by this, as the primary insect lineage that has only one pair of wings is flies (not that I have anything against flies, but I suspect bees would); bees and most other insects have two pairs of wings.
5) Whatever they've drawn over the eye: it looks like it's supposed to be an eyebrow, and I could see it as a Pitot tube, but it sure doesn't belong there.
6) There're no pollen baskets (corbiculae) on the hind legs; bees use these baskets to carry pollen back from flowers to their hive. Considering that the bee is busy visiting flowers during the commercial, and thus is most likely a foraging worker, it should definitely have pollen baskets.
For some great closeups of what honey bees actually look like, take a look at these SEMs or these videos of a bee feeding. Aren't they far cuter in real life?
Coming up next on Rhosgobel: rabbits don't really clamor for sugary cereals.